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AbstractThis is an extended summary of a talk given by the last named author at the Czecho-Slovake Number Theory Conference 2005, held at Malenovice in September 2005. It surveys some recent results concerning asymptotics for a class of arithmetic functions, including, e.g., the second moments of the number-of-divisors function d(n) and of the function r(n) which counts the number of ways to write a positive integer as a sum of two squares. For the proofs, reference is made to original articlesdoi:10.2478/s12175-008-0075-2 fatcat:u3zk5a5f5reu3orvbiqveblgnu